The Supreme Court will decide on Monday whether the two Italian marines charged with murdering a pair of Kerala fishermen should be investigated by the Central Bureau of Investigation (CBI) or the National Investigation Agency (NIA).
The government argued in court today that the CBI is "over-burdened" and that the NIA can complete the enquiry within 60 days.
Italy has repeatedly urged India for a swift trial.
Today, its lawyers argued in court that the NIA does not have jurisdiction for the investigation. Italy has been opposed to the NIA handling the case because of concerns that the agency has invoked maritime laws and charges that are punishable with a death sentence.
In March, India promised Rome that the death penalty would not apply and that the naval officers could serve the sentence at home, if convicted.
Those promises were made after Italy reneged on its commitment to return the marines to Delhi to stand trial. They had been permitted by the Supreme Court to travel home for four weeks. Suddenly, Rome announced they would not return, triggering a diplomatic crisis.
Massimiliano Latorre and Salvatore Girone flew to India on an Italian Air Force plane just hours before the Supreme Court deadline for their return expired.
The naval officers were guarding an Italian tanker when they say they mistook the fishermen for pirates and opened fire in February 2012. Italy says the shooting took place in international waters and India has no jurisdiction. New Delhi disagrees.